Transcript Introduction to Statistics

Introduction to Statistics
Osama A Samarkandi, PhD, RN
BSc, GMD, BSN, MSN, NIAC
Deanship of Skill development
Dec. 2nd-3rd, 2013
Objectives
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Definitions,
Type of Statistics,
Normal Distribution Function, and Curve,
Standard Deviation (σ), and Quality.
Definition
• Statistics: is a branch of applied mathematics
that deals with collection, organizing, and
interpreting data using well-defined procedure.
Type of Statistics
• There are two type of statistics; (Descriptive &
Inferential),
• Descriptive Statistics: are used to describe or
characterize data by summarizing them into more
understandable terms without losing or distorting
much of the information.
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Frequency Distributions,
Graphic Representation,
Central Tendency,
Variability or Scatter.
Type of Statistics
• Inferential Statistics: consist of a set of
statistical techniques that provide predictions
about population based on information in a
sample from that population.
• Probability,
• Population,
• Sample (i.e Random Sample, Convenience
Sample, .. etc.),
• Parameters.
Normal distribution function
Normal distribution Curve
Standard Deviation & Quality
Σ
% Within CI
% Outside CI
Fraction outside CI
1σ 68.2689492%
31.7310508%
1 / 3.1514872
2σ 95.4499736%
4.5500264%
1 / 21.977895
3σ 99.7300204%
0.2699796%
1 / 370.398
4σ 99.993666%
0.006334%
1 / 15,787
5σ 99.9999426697%
0.0000573303%
1 / 1,744,278
6σ 99.9999998027%
0.0000001973%
1 / 506,797,346
7σ 99.9999999997440% 0.000000000256%
1 / 390,682,215,445
Questions
Thank you !
Type of Test Required
Osama A Samarkandi, PhD, RN
BSc, GMD, BSN, MSN, NIAC
Deanship of Skill development
Dec. 2nd-3rd, 2013
Questions
Thank you !
Advanced Statistics
Power Analysis & Sample Size
Osama A Samarkandi, PhD, RN
BSc, GMD, BSN, MSN, NIAC
Deanship of Skill development
Dec. 2nd-3rd, 2013
Objectives
• Introduction to power analysis,
• Effect size, Degree of freedom, and Sample
size calculations,
• G-Power application.
What is power analysis
• Power analysis is a method of reducing the
• Risk of Type II errors and for estimating their
occurrence
• Power, by definition, is the ability to find a
statistically significant difference when the
null hypothesis is in fact false (UWM).
What is power analysis
• The power of a study is determined by three
factors:
• Sample size,
• Alpha level (degree of freedom), and
• Effect size.
What is power analysis
• The significance criterion; Other things being equal,
the more stringent this criterion, the lower the power.
• The sample size, N. As sample size increases, power
increases.
• The population effect size, gamma (γ). Gamma is a
measure of how wrong the null hypothesis is, that is,
how strong the effect of the independent variable is on
the dependent variable in the population.
• Power, or 1-β . This is the probability of rejecting
• the null hypothesis.
Sample size
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n  
 d Diff
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2
Sample size
• How much data do you need? That is, how
many subjects should you include in your
research.
• The answer to this question is very simple -the more data the better. The more data you
have, the more likely you are to reach a correct
decision and the less error there will be in your
estimates of parameters of interest
Sample size … Cont,
• Before you can answer the question “how many subjects do
I need,” you will have to answer several other questions,
such as:
• How much power do I want?
• What is the likely size (in the population) of the effect I am
trying to detect, or, what is smallest effect size that I would
consider of importance?
• What criterion of statistical significance will I employ?
• What test statistic will I employ?
• What is the standard deviation (in the population) of the
criterion variable?
• For correlated samples designs, what is the correlation (in
the population) between groups?
Effect size
 
2
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2
f 
2
1 
2
SSbetween
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SStotal
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n
Effect size
• Power analysis builds on the concept of an
effect size, which expresses the strength of
relationships among research variables.
G-Power
G-Power
• There are several different sorts of power analyses
• A Priori Power Analysis. This is an important part of planning
research. You determine how many cases you will need to have a
good chance of detecting an effect of a specified size with the
desired amount of power.
• A Posteriori Power Analysis. Also know as “post hoc” power
analysis. Here you find how much power you would have if you
had a specified number of cases. Is it “a posteriori” only in the
sense that you provide the number of number of cases, as if you
had already conducted the research.
G-Power
• Retrospective Power Analysis. Also known as
“observed power.” There are several types, but basically
this involves answering the following question: “If I
were to repeat this research, using the same methods and
the same number of cases, and if the size of the effect in
the population was exactly the same as it was in the
present sample, what would be the probability that I
would obtain significant results?”
References
• Faul, F., Erdfelder, E., Buchner, A., & Lang, A.G. (2009). Statistical power analyses using
G*Power 3.1: Tests for correlation and regression
analyses. Behavior Research Methods, 41, 11491160.
• Faul, F., Erdfelder, E., Lang, A.-G., & Buchner,
A. (2007). G*Power 3: A flexible statistical
power analysis program for the social, behavioral,
and biomedical sciences. Behavior Research
Methods, 39, 175-191.
References
• www.StatPages.net - This site provides links to a number of online power
calculators.
• Power analysis for ANOVA designs - an interactive site that computes that
calculates power or sample size needed to attain a given power for one
effect in a factorial ANOVA design. This particular program can be found
elsewhere on the web.
• PASS 2008 - a commercial site that allows you to download a 30 day trial
version of their program. This is the software that I use. I don't think it's
perfect, but I haven't come across anything that I think is better. Unlike
many programs, PASS allows users to compute power for repeated
measures designs.
• SPSS makes a program called SamplePower. I have only take a cursory
look at it, and was disappointed that it didn't include repeated measures
designs. However, one nice feature of the software is that it will output a
complete report on your computer screen which you can then cut and paste
into another document.
Questions
Thank you !